"For information about the improved Process Portal application that is introduced in IBM BPM 8.5.7, see Process Portal: What's New in IBM Business Process Manager V8.5.7. The Process Portal application for IBM BPM 8.5.6 and earlier is now referred to as Heritage Process Portal.
Note: If you need to use the Heritage Process Portal while training users for the new Process Portal, use the /HeritagePortal context root instead of the /ProcessPortal context root."

In other words, the heritage Process Portal is the user interface as it existed prior to BPM 8.5.7. It is only there to allow easier upgrade experience while transitioning to the new user interface.

There is a responsive Portal that is available ootb in IBM BPM starting IBM BPM 857.
There is also a Heritage Portal available in BPM 857 (you need to configure it to run) and that is an old-style Portal that was available since IBM BPM 8.0.x.